package com.koala.learn.utils;

import java.util.Objects;

public class Complex {
        private final double re;   // the real part  
        private final double im;   // the imaginary part  
  
        // create a new object with the given real and imaginary parts  
        public Complex(double real, double imag) {  
            re = real;  
            im = imag;  
        }  
  
        // return a string representation of the invoking Complex object  
        public String toString() {  
            if (im == 0) return re + "";  
            if (re == 0) return im + "i";  
            if (im <  0) return re + " - " + (-im) + "i";  
            return re + " + " + im + "i";  
        }  
  
        // return abs/modulus/magnitude  
        public double abs() {  
            return Math.hypot(re, im);  
        }  
  
        // return angle/phase/argument, normalized to be between -pi and pi  
        public double phase() {  
            return Math.atan2(im, re);  
        }  
  
        // return a new Complex object whose value is (this + b)  
        public Complex plus(Complex b) {  
            Complex a = this;             // invoking object  
            double real = a.re + b.re;  
            double imag = a.im + b.im;  
            return new Complex(real, imag);  
        }  
  
        // return a new Complex object whose value is (this - b)  
        public Complex minus(Complex b) {  
            Complex a = this;  
            double real = a.re - b.re;  
            double imag = a.im - b.im;  
            return new Complex(real, imag);  
        }  
  
        // return a new Complex object whose value is (this * b)  
        public Complex times(Complex b) {  
            Complex a = this;  
            double real = a.re * b.re - a.im * b.im;  
            double imag = a.re * b.im + a.im * b.re;  
            return new Complex(real, imag);  
        }  
  
        // return a new object whose value is (this * alpha)  
        public Complex scale(double alpha) {  
            return new Complex(alpha * re, alpha * im);  
        }  
  
        // return a new Complex object whose value is the conjugate of this  
        public Complex conjugate() {  
            return new Complex(re, -im);  
        }  
  
        // return a new Complex object whose value is the reciprocal of this  
        public Complex reciprocal() {  
            double scale = re*re + im*im;  
            return new Complex(re / scale, -im / scale);  
        }  
  
        // return the real or imaginary part  
        public double re() { return re; }  
        public double im() { return im; }  
  
        // return a / b  
        public Complex divides(Complex b) {  
            Complex a = this;  
            return a.times(b.reciprocal());  
        }  
  
        // return a new Complex object whose value is the complex exponential of this  
        public Complex exp() {  
            return new Complex(Math.exp(re) * Math.cos(im), Math.exp(re) * Math.sin(im));  
        }  
  
        // return a new Complex object whose value is the complex sine of this  
        public Complex sin() {  
            return new Complex(Math.sin(re) * Math.cosh(im), Math.cos(re) * Math.sinh(im));  
        }  
  
        // return a new Complex object whose value is the complex cosine of this  
        public Complex cos() {  
            return new Complex(Math.cos(re) * Math.cosh(im), -Math.sin(re) * Math.sinh(im));  
        }  
  
        // return a new Complex object whose value is the complex tangent of this  
        public Complex tan() {  
            return sin().divides(cos());  
        }  
          
  
  
        // a static version of plus  
        public static Complex plus(Complex a, Complex b) {  
            double real = a.re + b.re;  
            double imag = a.im + b.im;  
            Complex sum = new Complex(real, imag);  
            return sum;  
        }  
  
        // See Section 3.3.  
        public boolean equals(Object x) {  
            if (x == null) return false;  
            if (this.getClass() != x.getClass()) return false;  
            Complex that = (Complex) x;  
            return (this.re == that.re) && (this.im == that.im);  
        }  
  
        // See Section 3.3.  
        public int hashCode() {  
            return Objects.hash(re, im);
        }  
  
        // sample client for testing  
        public static void main(String[] args) {  
            Complex a = new Complex(5.0, 6.0);  
            Complex b = new Complex(-3.0, 4.0);  
  
            System.out.println("a            = " + a);  
            System.out.println("b            = " + b);  
            System.out.println("Re(a)        = " + a.re());  
            System.out.println("Im(a)        = " + a.im());  
            System.out.println("b + a        = " + b.plus(a));  
            System.out.println("a - b        = " + a.minus(b));  
            System.out.println("a * b        = " + a.times(b));  
            System.out.println("b * a        = " + b.times(a));  
            System.out.println("a / b        = " + a.divides(b));  
            System.out.println("(a / b) * b  = " + a.divides(b).times(b));  
            System.out.println("conj(a)      = " + a.conjugate());  
            System.out.println("|a|          = " + a.abs());  
            System.out.println("tan(a)       = " + a.tan());  
        }  
}  